Abstract
Silicate melts are very active in the interior of the Earth and other terrestrial planets, and are important carriers for the transport of material and energy. The determination of the equation of state (EOS) for silicate melts and the acquisition of a precise quantitative relationship between molar volume (or density) and temperature, pressure, and composition is essential for simulating the generation, migration, and eruption processes of magmas and the evolution of the magma ocean stage during the early formation of the Earth and other terrestrial planets, for calculating and modeling the phase equilibria involving silicate melts, and for revealing the variation of the microstructure of silicate melts with pressure. However, it is experimentally challenging to determine the volumetric properties of silicate melts and the accumulated density data at high pressure are still very limited due to a series of problems such as: the high liquidus temperature of silicate rocks; proneness for silicate melts to react with sample capsules to change the melt composition; and proneness for melts to flow and leak during the high pressure and high temperature experiments. In recent years, there is rapid progress in the high pressure and high temperature experimental techniques, in terms of not only the extension of temperature and pressure ranges but also the improvement on the accuracy of measurements, and the emergence of new methods for in-situ measurements. Here, we review the widely-used theoretical models of ambient-pressure and high-pressure EOS for silicate melts, and illustrate some problems that need to be solved urgently: (1) the room pressure EOS for iron- and titanium-bearing silicate melts needs to be improved; (2) the partial molar properties of the H2O and CO2 components in silicate melts containing volatile components may vary markedly with the melt composition, which need to be addressed in high-pressure EOS; (3) how the formulation and applicable range of EOS correspond to changes in melt structure and compression mechanism requires further study. We highlight the basic principle and applicable range of various methods for determining the EOS for silicate melts, and compare the advantages and disadvantages of doublebob Archimedes method, fusion curve analysis, shock compression experiments, sink-float method, X-ray absorption, X-ray diffraction and ultrasonic interferometry. Future trends in this field are to develop experimental techniques for in situ measurements on melt density or sound velocity at high temperature and high pressure and to accumulate more experimental data, and on the other hand, to improve the theoretical models of the EOS for silicate melts by a combination of research on the microstructure and compression mechanisms of silicate melts.
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References
Agee C B. 1998. Crystal-liquid density inversions in terrestrial and lunar magmas. Phys Earth Planet Inter, 107: 63–74
Agee C B. 2008. Static compression of hydrous silicate melt and the effect of water on planetary differentiation. Earth Planet Sci Lett, 265: 641–654
Agee C B, Walker D. 1988. Static compression and olivine flotation in ultrabasic silicate liquid. J Geophys Res, 93: 3437–3449
Agee C B, Walker D. 1993. Olivine flotation in mantle melt. Earth Planet Sci Lett, 114: 315–324
Ahart M, Karandikar A, Gramsch S, Boehler R, Hemley R J. 2014. High PT Brillouin scattering study of H2O melting to 26 GPa. High Pressure Res, 34: 327–336
Ahrens T J. 1993. Equation of state. In: Asay J R, Shahinpoor M, eds. High-Pressure Shock Compression of Solids. New York: Springer-Verlag. 75–113
Ai Y H, Lange R. 2004a. An ultrasonic frequency sweep interferometer for liquids at high temperature: 1. Acoustic model. J Geophys Res, 109: 12203
Ai Y H, Lange R. 2004b. An ultrasonic frequency sweep interferometer for liquids at high temperature: 2. Mechanical assembly, signal processing, and application. J Geophys Res, 109: B12204
Ai Y, Lange R A. 2008. New acoustic velocity measurements on CaOMgO-Al2O3-SiO2 liquids: Reevaluation of the volume and compressibility of CaMgSi2O6-CaAl2Si2O8 liquids to 25 GPa. J Geophys Res, 113: 04203
Álvarez-Murga M, Perrillat J P, Le Godec Y, Bergame F, Philippe J, King A, Guignot N, Mezouar M, Hodeau J L. 2017. Development of synchrotron X-ray micro-tomography under extreme conditions of pressure and temperature. J Synchrotron Radiat, 24: 240–247
Angel R J. 2000. Equations of state. Rev Mineral Geochem, 41: 35–59
Angel R J, Gonzalez-Platas J, Alvaro M. 2014. EosFit7c and a Fortran module (library) for equation of state calculations. Z Krist-Cryst Mater, 229: 405–419
Asimow P D. 2012. Shock compression of preheated silicate liquids: Apparent universality of increasing Grüneisen parameter upon compression. In: Elert M L, Buttler W T, Borg J P, Jordan J L, Vogler T J, eds. AIP Conference Proceedings. Melville: American Institute of Physics. 1426: 887–890
Asimow P D, Ahrens T J. 2010. Shock compression of liquid silicates to 125 GPa: The anorthite-diopside join. J Geophys Res, 115: B10209
Ayrinhac S, Gauthier M, Le Marchand G, Morand M, Bergame F, Decremps F. 2015. Thermodynamic properties of liquid gallium from picosecond acoustic velocity measurements. J Phys-Condens Matter, 27: 275103
Bajgain S, Ghosh D B, Karki B B. 2015. Structure and density of basaltic melts at mantle conditions from first-principles simulations. Nat Commun, 6: 8578
Bassett W A. 2009. Diamond anvil cell, 50th birthday. High Pressure Res, 29: 163–186
Boslough M B, Asay J R. 1993. Basic principles of shock compression. In: Asay J R, Shahinpoor M, eds. High-Pressure Shock Compression of Solids. New York: Springer-Verlag. 7–42
Carlson R W, Garnero E, Harrison T M, Li J, Manga M, McDonough W F, Mukhopadhyay S, Romanowicz B, Rubie D, Williams Q, Zhong S. 2014. How did early Earth become our modern world? Annu Rev Earth Planet Sci, 42: 151–178
Chantel J, Manthilake G, Andrault D, Novella D, Yu T, Wang Y. 2016. Experimental evidence supports mantle partial melting in the asthenosphere. Sci Adv, 2: e1600246
Chen G Q, Ahrens T J. 1998. Radio frequency heating coils for shock wave experiments. In: Wentzcovitch R M, Hemley R J, Nellis W J, Yu P Y, eds. High-Pressure Materials Research. Materials Research Society Symposium Proceedings. Warrendale: Materials Research Society. 499: 63–71
Chen G Q, Ahrens T J, Stolper E M. 2002. Shock-wave equation of state of molten and solid fayalite. Phys Earth Planet Inter, 134: 35–52
Chevrel M O, Giordano D, Potuzak M, Courtial P, Dingwell D B. 2013. Physical properties of CaAl2Si2O8-CaMgSi2O6-FeO-Fe2O3 melts: Analogues for extra-terrestrial basalt. Chem Geol, 346: 93–105
Circone S, Agee C B. 1996. Compressibility of molten high-Ti mare glass: Evidence for crystal-liquid density inversions in the lunar mantle. Geochim Cosmochim Acta, 60: 2709–2720
Cochain B, Sanloup C, Leroy C, Kono Y. 2017. Viscosity of mafic magmas at high pressures. Geophys Res Lett, 44: 818–826
Courtial P, Dingwell D B. 1999. Densities of melts in the CaO-MgO-Al2O3-SiO2 system. Am Miner, 84: 465–476
Courtial P. 2005. High-temperature density of lanthanide-bearing Na-silicate melts: Partial molar volumes for Ce2O3, Pr2O3, Nd2O3, Sm2O3, Eu2O3, Gd2O3, Tb2O3, Dy2O3, Ho2O3, Er2O3, Tm2O3, and Yb2O3. Am Miner, 90: 1597–1605
Crépisson C, Morard G, Bureau H, Prouteau G, Morizet Y, Petitgirard S, Sanloup C. 2014. Magmas trapped at the continental lithosphere-asthenosphere boundary. Earth Planet Sci Lett, 393: 105–112
Decremps F, Belliard L, Couzinet B, Vincent S, Munsch P, Le Marchand G, Perrin B. 2009. Liquid mercury sound velocity measurements under high pressure and high temperature by picosecond acoustics in a diamond anvils cell. Rev Sci Instrum, 80: 073902
Dubrovinsky L, Dubrovinskaia N, Prakapenka V B, Abakumov A M. 2012. Implementation of micro-ball nanodiamond anvils for high-pressure studies above 6 Mbar. Nat Commun, 3: 1163
Duncan M S, Agee C B. 2011. The partial molar volume of carbon dioxide in peridotite partial melt at high pressure. Earth Planet Sci Lett, 312: 429–436
Dziewonski A M, Anderson D L. 1981. Preliminary reference earth model. Phys Earth Planet Inter, 25: 297–356
Eggert J H, Weck G, Loubeyre P, Mezouar M. 2002. Quantitative structure factor and density measurements of high-pressure fluids in diamond anvil cells by X-ray diffraction: Argon and water. Phys Rev B, 65: 174105
Elkins-Tanton L T. 2012. Magma oceans in the inner solar system. Annu Rev Earth Planet Sci, 40: 113–139
Fortov V E, Lomonosov I V. 2010. Shock waves and equations of state of matter. Shock Waves, 20: 53–71
Funakoshi K, Nozawa A. 2012. Development of a method for measuring the density of liquid sulfur at high pressures using the falling-sphere technique. Rev Sci Instrum, 83: 103908
Funamori N, Sato T. 2010. Density contrast between silicate melts and crystals in the deep mantle: An integrated view based on static-compression data. Earth Planet Sci Lett, 295: 435–440
Ghiorso M S. 2004a. An equation of state for silicate melts. I. Formulation of a general model. Am J Sci, 304: 637–678
Ghiorso M S. 2004b. An equation of state for silicate melts. III. Analysis of stoichiometric liquids at elevated pressure: Shock compression data, molecular dynamics simulations and mineral fusion curves. Am J Sci, 304: 752–810
Ghiorso M S. 2004c. An equation of state for silicate melts. IV. Calibration of a multicomponent mixing model to 40 GPa. Am J Sci, 304: 811–838
Ghiorso M S, Kress V C. 2004. An equation of state for silicate melts. II. Calibration of volumetric properties at 105 Pa. Am J Sci, 304: 679–751
Ghosh S, Ohtani E, Litasov K, Suzuki A, Sakamaki T. 2007. Stability of carbonated magmas at the base of the Earth’s upper mantle. Geophys Res Lett, 34: L22312
Gonzalez-Platas J, Alvaro M, Nestola F, Angel R. 2016. EosFit7-GUI: A new graphical user interface for equation of state calculations, analyses and teaching. J Appl Crystlogr, 49: 1377–1382
Guo X. 2013. Density and compressibility of FeO-bearing silicate melt: Relevance to magma behavior in the Earth. Doctoral Dissertation. Ann Arbor: University of Michigan
Guo X, Lange R A, Ai Y. 2013. The density and compressibility of CaOFeO-SiO2 liquids at one bar: Evidence for four-coordinated Fe2+ in the CaFeO2 component. Geochim Cosmochim Acta, 120: 206–219
Guo X, Lange R A, Ai Y. 2014. Density and sound speed measurements on model basalt (An-Di-Hd) liquids at one bar: New constraints on the partial molar volume and compressibility of the FeO component. Earth Planet Sci Lett, 388: 283–292
Harvey J P, Asimow P D. 2015. Current limitations of molecular dynamic simulations as probes of thermo-physical behavior of silicate melts. Am Miner, 100: 1866–1882
Hong X, Shen G, Prakapenka V B, Rivers M L, Sutton S R. 2007. Density measurements of noncrystalline materials at high pressure with diamond anvil cell. Rev Sci Instrum, 78: 103905
Huang F, Wu Z, Huang S, Wu F. 2014. First-principles calculations of equilibrium silicon isotope fractionation among mantle minerals. Geochim Cosmochim Acta, 140: 509–520
Jacobsen S D, Reichmann H J, Kantor A, Spetzler H A. 2005. A gigahertz ultrasonic interferometer for the diamond anvil cell and high-pressure elasticity of some iron-oxide minerals. In: Chen J, Wang Y, Duffy T S, Shen G, Dobrzhinetskaya L F, eds. Advances in High-Pressure Technology for Geophysical Applications. Amsterdam: Elsevier. 25–48
Jacobsen S D, Spetzler H, Reichmann H J, Smyth J R. 2004. Shear waves in the diamond-anvil cell reveal pressure-induced instability in (Mg, Fe)O. Proc Natl Acad Sci USA, 101: 5867–5871
Jacobsen S D, Spetzler H A, Reichmann H J, Smyth J R, Mackwell S J, Angel R J, Bassett W A. 2002. Gigahertz ultrasonic interferometry at high P and T: New tools for obtaining a thermodynamic equation of state. J Phys-Condens Matter, 14: 11525–11530
Jing Z, Karato S. 2008. Compositional effect on the pressure derivatives of bulk modulus of silicate melts. Earth Planet Sci Lett, 272: 429–436
Jing Z, Karato S. 2009. The density of volatile bearing melts in the Earth’s deep mantle: The role of chemical composition. Chem Geol, 262: 100–107
Jing Z, Karato S. 2011. A new approach to the equation of state of silicate melts: An application of the theory of hard sphere mixtures. Geochim Cosmochim Acta, 75: 6780–6802
Jing Z, Karato S. 2012. Effect of H2O on the density of silicate melts at high pressures: Static experiments and the application of a modified hard-sphere model of equation of state. Geochim Cosmochim Acta, 85: 357–372
Jing Z, Wang Y, Kono Y, Yu T, Sakamaki T, Park C, Rivers M L, Sutton S R, Shen G. 2014. Sound velocity of Fe-S liquids at high pressure: Implications for the Moon’s molten outer core. Earth Planet Sci Lett, 396: 78–87
Jones A P, Genge M, Carmody L. 2013. Carbonate melts and carbonatites. Rev Mineral Geochem, 75: 289–322
Kanzaki M, Kurita K, Fujii T, Kato T, Shimomura O, Akimoto S. 1987. A new technique to measure the viscosity and density of silicate melts at high pressure. In: Manghnani M H, Syono Y, eds. High-Pressure Research in Mineral Physics. Tokyo: Terrapub. 195–200
Karki B B. 2010. First-principles molecular dynamics simulations of silicate melts: Structural and dynamical properties. Rev Mineral Geochem, 71: 355–389
Karki B B. 2015. First-principles computation of mantle materials in crystalline and amorphous phases. Phys Earth Planet Inter, 240: 43–69
Katayama Y, Tsuji K, Chen J Q, Koyama N, Kikegawa T, Yaoita K, Shimomura O. 1993. Density of liquid tellurium under high pressure. J Non-Cryst Solids, 156–158: 687–690
Katayama Y, Tsuji K, Kanda H, Nosaka H, Yaoita K, Kikegawa T, Shimomura O. 1996. Density of liquid tellurium under pressure. J Non-Cryst Solids, 205–207: 451–454
Katayama Y, Tsuji K, Shimomura O, Kikegawa T, Mezouar M, Martinez-Garcia D, Besson J M, Häusermann D, Hanfland M. 1998. Density measurements of liquid under high pressure and high temperature. J Synchrotron Radiat, 5: 1023–1025
Knoche R, Luth R W. 1996. Density measurements on melts at high pressure using the sink/float method: Limitations and possibilities. Chem Geol, 128: 229–243
Kono Y, Kenney-Benson C, Shibazaki Y, Park C, Shen G, Wang Y. 2015. High-pressure viscosity of liquid Fe and FeS revisited by falling sphere viscometry using ultrafast X-ray imaging. Phys Earth Planet Inter, 241: 57–64
Kono Y, Park C, Kenney-Benson C, Shen G, Wang Y. 2014. Toward comprehensive studies of liquids at high pressures and high temperatures: Combined structure, elastic wave velocity, and viscosity measurements in the Paris-Edinburgh cell. Phys Earth Planet Inter, 228: 269–280
Kuwabara S, Terasaki H, Nishida K, Shimoyama Y, Takubo Y, Higo Y, Shibazaki Y, Urakawa S, Uesugi K, Takeuchi A, Kondo T. 2016. Sound velocity and elastic properties of Fe-Ni and Fe-Ni-C liquids at high pressure. Phys Chem Miner, 43: 229–236
Lange R A. 1994. The effect of H2O, CO2 and F on the density and viscosity of silicate melts. Rev Mineral, 30: 331–369
Lange R A. 1996. Temperature independent thermal expansivities of sodium aluminosilicate melts between 713 and 1835 K. Geochim Cosmochim Acta, 60: 4989–4996
Lange R A. 1997. A revised model for the density and thermal expansivity of K2O-Na2O-CaO-MgO-Al2O3-SiO2 liquids from 700 to 1900 K: Extension to crustal magmatic temperatures. Contrib Mineral Petrol, 130: 1–11
Lange R A. 2003. The fusion curve of albite revisited and the compressibility of NaAlSi3O8 liquid with pressure. Am Miner, 88: 109–120
Lange R A. 2007. The density and compressibility of KAlSi3O8 liquid to 6.5 GPa. Am Miner, 92: 114–123
Lange R A, Carmichael I S E. 1987. Densities of Na2O-K2O-CaO-MgOFeO-Fe2O3-Al2O3-TiO2-SiO2 liquids: New measurements and derived partial molar properties. Geochim Cosmochim Acta, 51: 2931–2946
Lange R A, Carmichael I S E. 1990. Thermodynamic properties of silicate liquids with emphasis on density, thermal-expansion and compressibility. Rev Mineral, 24: 25–64
Lesher, C E, Spera, F J. 2015. Chapter 5–thermodynamic and transport properties of silicate melts and magma. In: Sigurdsson H, ed. The Encyclopedia of Volcanoes, 113–141
Li B, Kung J, Liebermann R C. 2004. Modern techniques in measuring elasticity of Earth materials at high pressure and high temperature using ultrasonic interferometry in conjunction with synchrotron X-radiation in multi-anvil apparatus. Phys Earth Planet Inter, 143: 559–574
Li B, Liebermann R C. 2007. Indoor seismology by probing the Earth’s interior by using sound velocity measurements at high pressures and temperatures. Proc Natl Acad Sci USA, 104: 9145–9150
Li B, Liebermann R C. 2014. Study of the Earth’s interior using measurements of sound velocities in minerals by ultrasonic interferometry. Phys Earth Planet Inter, 233: 135–153
Li B, Liu W. 2010. Advanced elasticity and density measurements on melts at mantle pressures using ultrasonic interferometry and synchrotron Xradiation. AGU Fall Meeting, abstract #MR44A-02
Liebermann R C. 2011. Multi-anvil, high pressure apparatus: A half-century of development and progress. High Pressure Res, 31: 493–532
Liu L, Bi Y, Xu J A. 2016. Latest developments in experimental research on structural and physical properties of liquids under extreme conditions (in Chinese). Chin J High Pressure Phys, 30: 7–19
Liu Q, Lange R A. 2001. The partial molar volume and thermal expansivity of TiO2 in alkali silicate melts: Systematic variation with Ti coordination. Geochim Cosmochim Acta, 65: 2379–2393
Liu Q, Lange R A. 2006. The partial molar volume of Fe2O3 in alkali silicate melts: Evidence for an average Fe3+ coordination number near five. Am Miner, 91: 385–393
Liu Q, Lange R A, Ai Y. 2007a. Acoustic velocity measurements on Na2OTiO2-SiO2 liquids: Evidence for a highly compressible TiO2 component related to five-coordinated Ti. Geochim Cosmochim Acta, 71: 4314–4326
Liu Q, Tenner T J, Lange R A. 2007b. Do carbonate liquids become denser than silicate liquids at pressure? Constraints from the fusion curve of K2CO3 to 3.2 GPa. Contrib Mineral Petrol, 153: 55–66
Malfait W J, Sanchez-Valle C, Ardia P, Medard E, Lerch P. 2011. Amorphous materials: Properties, structure, and durability: Compositional dependent compressibility of dissolved water in silicate glasses. Am Miner, 96: 1402–1409
Malfait W J, Seifert R, Petitgirard S, Mezouar M, Sanchez-Valle C. 2014a. The density of andesitic melts and the compressibility of dissolved water in silicate melts at crustal and upper mantle conditions. Earth Planet Sci Lett, 393: 31–38
Malfait W J, Seifert R, Petitgirard S, Perrillat J P, Mezouar M, Ota T, Nakamura E, Lerch P, Sanchez-Valle C. 2014b. Supervolcano eruptions driven by melt buoyancy in large silicic magma chambers. Nat Geosci, 7: 122–125
Matsukage K N, Jing Z, Karato S I. 2005. Density of hydrous silicate melt at the conditions of Earth’s deep upper mantle. Nature, 438: 488–491
Miller G H, Ahrens T J, Stolper E M. 1988. The equation of state of molybdenum at 1400°C. J Appl Phys, 63: 4469–4475
Miller G H, Stolper E M, Ahrens T J. 1991. The equation of state of a molten komatiite: 1. Shock wave compression to 36 GPa. J Geophys Res, 96: 11831–11848
Morard G, Garbarino G, Antonangeli D, Andrault D, Guignot N, Siebert J, Roberge M, Boulard E, Lincot A, Denoeud A, Petitgirard S. 2014. Density measurements and structural properties of liquid and amorphous metals under high pressure. High Pressure Res, 34: 9–21
Mueller H J, Roetzler K, Schilling F R, Lathe C, Wehber M. 2010. Techniques for measuring the elastic wave velocities of melts and partial molten systems under high pressure conditions. J Phys Chem Solids, 71: 1108–1117
Nakajima Y, Imada S, Hirose K, Komabayashi T, Ozawa H, Tateno S, Tsutsui S, Kuwayama Y, Baron A Q R. 2015. Carbon-depleted outer core revealed by sound velocity measurements of liquid iron-carbon alloy. Nat Commun, 6: 8942
Ni H. 2013. Advances and application in physicochemical properties of silicate melts. Chin Sci Bull, 58: 865–890
Ni H, Zhang L, Guo X. 2016. Water and partial melting of Earth’s mantle. Sci China Earth Sci, 59: 720–730
Nishida K, Kono Y, Terasaki H, Takahashi S, Ishii M, Shimoyama Y, Higo Y, Funakoshi K, Irifune T, Ohtani E. 2013. Sound velocity measurements in liquid Fe-S at high pressure: Implications for Earth’s and lunar cores. Earth Planet Sci Lett, 362: 182–186
Nishida K, Suzuki A, Terasaki H, Shibazaki Y, Higo Y, Kuwabara S, Shimoyama Y, Sakurai M, Ushioda M, Takahashi E, Kikegawa T, Wakabayashi D, Funamori N. 2016. Towards a consensus on the pressure and composition dependence of sound velocity in the liquid Fe-S system. Phys Earth Planet Inter, 257: 230–239
Ochs F A, Lange R A. 1997. The partial molar volume, thermal expansivity, and compressibility of H2O in NaAlSi3O8 liquid: New measurements and an internally consistent model. Contrib Mineral Petrol, 129: 155–165
Ochs F A, Lange R A. 1999. The density of hydrous magmatic liquids. Science, 283: 1314–1317
Ohira I, Murakami M, Kohara S, Ohara K, Ohtani E. 2016. Ultrahighpressure acoustic wave velocities of SiO2-Al2O3 glasses up to 200 GPa. Prog Earth Planet Sci, 3: 18
Ohtani E. 2009. Melting relations and the equation of state of magmas at high pressure: Application to geodynamics. Chem Geol, 265: 279–288
Ohtani E, Maeda M. 2001. Density of basaltic melt at high pressure and stability of the melt at the base of the lower mantle. Earth Planet Sci Lett, 193: 69–75
Ohtani E, Suzuki A, Ando R, Urakawa S, Funakoshi K, Katayama Y. 2005. Viscosity and density measurements of melts and glasses at high pressure and temperature by using the multi-anvil apparatus and synchrotron X-ray radiation. In: Chen J, Wang Y, Duffy T S, Shen G, Dobrzhinetskaya L F, eds. Advances in High-Pressure Technology for Geophysical Applications. Amsterdam: Elsevier. 195–209
Ohtani E, Suzuki A, Kato T. 1993. Flotation of olivine in the peridotite melt at high pressure. Proc Jpn Acad Ser B-Phys Biol Sci, 69: 23–28
Petitgirard S. 2017. Density and structural changes of silicate glasses under high pressure. High Pressure Res, 37: 200–213
Petitgirard S, Malfait W J, Sinmyo R, Kupenko I, Hennet L, Harries D, Dane T, Burghammer M, Rubie D C. 2015. Fate of MgSiO3 melts at core-mantle boundary conditions. Proc Natl Acad Sci USA, 112: 14186–14190
Poirier J. 2000. Introduction to the Physics of the Earth’s Interior. 2nd ed. Cambridge: Cambridge University Press. 312
Reichmann H J, Jacobsen S D, Ballaran T B. 2013. Elasticity of franklinite and trends for transition-metal oxide spinels. Am Miner, 98: 601–608
Rigden S M, Ahrens T J, Stolper E M. 1984. Densities of liquid silicates at high pressures. Science, 226: 1071–1074
Rigden S M, Ahrens T J, Stolper E M. 1988. Shock compression of molten silicate: Results for a model basaltic composition. J Geophys Res, 93: 367–382
Rigden S M, Ahrens T J, Stolper E M. 1989. High-pressure equation of state of molten anorthite and diopside. J Geophys Res, 94: 9508–9522
Rivers M L, Carmichael I S E. 1987. Ultrasonic studies of silicate melts. J Geophys Res, 92: 9247–9270
Rowan L R. 1993. I. Equation of state of molten mid-ocean ridge basalt II. Structure of Kilauea volcano, Hawaii. Doctoral Dissertation. Pasadena: California Institute of Technology
Sakamaki T, Ohtani E, Urakawa S, Suzuki A, Katayama Y. 2009. Measurement of hydrous peridotite magma density at high pressure using the X-ray absorption method. Earth Planet Sci Lett, 287: 293–297
Sakamaki T, Ohtani E, Urakawa S, Suzuki A, Katayama Y. 2010a. Density of dry peridotite magma at high pressure using an X-ray absorption method. Am Miner, 95: 144–147
Sakamaki T, Ohtani E, Urakawa S, Suzuki A, Katayama Y, Zhao D. 2010b. Density of high-Ti basalt magma at high pressure and origin of heterogeneities in the lunar mantle. Earth Planet Sci Lett, 299: 285–289
Sakamaki T, Ohtani E, Urakawa S, Terasaki H, Katayama Y. 2011. Density of carbonated peridotite magma at high pressure using an X-ray absorption method. Am Miner, 96: 553–557
Sakamaki T, Suzuki A, Ohtani E. 2006. Stability of hydrous melt at the base of the Earth’s upper mantle. Nature, 439: 192–194
Sakamaki T, Suzuki A, Ohtani E, Terasaki H, Urakawa S, Katayama Y, Funakoshi K I, Wang Y, Hernlund J W, Ballmer M D. 2013. Ponded melt at the boundary between the lithosphere and asthenosphere. Nat Geosci, 6: 1041–1044
Sanloup C. 2016. Density of magmas at depth. Chem Geol, 429: 51–59
Sanloup C, Drewitt J W E, Crépisson C, Kono Y, Park C, McCammon C, Hennet L, Brassamin S, Bytchkov A. 2013a. Structure and density of molten fayalite at high pressure. Geochim Cosmochim Acta, 118: 118–128
Sanloup C, Drewitt J W E, Konôpková Z, Dalladay-Simpson P, Morton D M, Rai N, van Westrenen W, Morgenroth W. 2013b. Structural change in molten basalt at deep mantle conditions. Nature, 503: 104–107
Sato T, Funamori N. 2008. Sixfold-coordinated amorphous polymorph of SiO2 under high pressure. Phys Rev Lett, 101: 255502
Schmandt B, Jacobsen S D, Becker T W, Liu Z, Dueker K G. 2014. Dehydration melting at the top of the lower mantle. Science, 344: 1265–1268
Schmerr N. 2012. The Gutenberg discontinuity: Melt at the lithosphereasthenosphere boundary. Science, 335: 1480–1483
Secco R A, Manghnani M H, Liu T C. 1991a. The bulk modulus-attenuation-viscosity systematics of diopside-anorthite melts. Geophys Res Lett, 18: 93–96
Secco R A, Manghnani M H, Liu T. 1991b. Velocities and compressibilities of komatiitic melts. Geophys Res Lett, 18: 1397–1400
Seifert R, Malfait W J, Lerch P, Sanchez-Valle C. 2013a. Partial molar volume and compressibility of dissolved CO2 in glasses with magmatic compositions. Chem Geol, 358: 119–130
Seifert R, Malfait W J, Petitgirard S, Sanchez-Valle C. 2013b. Density of phonolitic magmas and time scales of crystal fractionation in magma chambers. Earth Planet Sci Lett, 381: 12–20
Shen G, Mao H K. 2017. High-pressure studies with X-rays using diamond anvil cells. Rep Prog Phys, 80: 016101
Shen G, Sata N, Newville M, Rivers M L, Sutton S R. 2002. Molar volumes of molten indium at high pressures measured in a diamond anvil cell. Appl Phys Lett, 81: 1411–1413
Shen G, Wang Y. 2014. High-pressure apparatus integrated with synchrotron radiation. Rev Mineral Geochem, 78: 745–777
Shimoyama Y, Terasaki H, Urakawa S, Takubo Y, Kuwabara S, Kishimoto S, Watanuki T, Machida A, Katayama Y, Kondo T. 2016. Thermoelastic properties of liquid Fe-C revealed by sound velocity and density measurements at high pressure. J Geophys Res-Solid Earth, 121: 7984–7995
Smith J R, Agee C B. 1997. Compressibility of molten “green glass” and crystal-liquid density crossovers in low-Ti lunar magma. Geochim Cosmochim Acta, 61: 2139–2145
Stixrude L, de Koker N, Sun N, Mookherjee M, Karki B B. 2009. Thermodynamics of silicate liquids in the deep Earth. Earth Planet Sci Lett, 278: 226–232
Stolper E, Hager B H, Walker D, Hays J F. 1981. Melt segregation from partially molten source regions: The importance of melt density and source region size. J Geophys Res, 86: 6261–6271
Suzuki A, Ohtani E. 2003. Density of peridotite melts at high pressure. Phys Chem Miner, 30: 449–456
Suzuki A, Ohtani E, Kato T. 1995. Flotation of diamond in mantle melt at high pressure. Science, 269: 216–218
Suzuki A, Ohtani E, Kato T. 1998. Density and thermal expansion of a peridotite melt at high pressure. Phys Earth Planet Inter, 107: 53–61
Suzuki A, Ohtani E, Terasaki H, Sakamaki T, Nishida K, Funakoshi K. 2007. In situ buoyancy test for the density measurement of basaltic liquid at high pressure and high temperature. AGU Fall Meeting, abstracts #MR13B-1258
Tauzin B, Debayle E, Wittlinger G. 2010. Seismic evidence for a global low-velocity layer within the Earth’s upper mantle. Nat Geosci, 3: 718–721
Tenner T J, Lange R A, Downs R T. 2007. The albite fusion curve reexamined: New experiments and the high-pressure density and compressibility of high albite and NaAlSi3O8 liquid. Am Miner, 92: 1573–1585
Thibodeau E, Gheribi A E, Jung I H. 2016a. A structural molar volume model for oxide melts part I: Li2O-Na2O-K2O-MgO-CaO-MnO-PbOAl2O3-SiO2 melts—Binary systems. Metall Mater Trans B, 47: 1147–1164
Thibodeau E, Gheribi A E, Jung I H. 2016b. A structural molar volume model for oxide melts part II: Li2O-Na2O-K2O-MgO-CaO-MnO-PbOAl2O3-SiO2 melts—Ternary and multicomponent systems. Metall Mater Trans B, 47: 1165–1186
Thibodeau E, Gheribi A E, Jung I H. 2016c. A structural molar volume model for oxide melts part III: Fe oxide-containing melts. Metall Mater Trans B, 47: 1187–1202
Thomas C W, Asimow P D. 2013a. Preheated shock experiments in the molten CaAl2Si2O8-CaFeSi2O6-CaMgSi2O6 ternary: A test for linear mixing of liquid volumes at high pressure and temperature. J Geophys Res-Solid Earth, 118: 3354–3365
Thomas C W, Asimow P D. 2013b. Direct shock compression experiments on premolten forsterite and progress toward a consistent high-pressure equation of state for CaO-MgO-Al2O3-SiO2-FeO liquids. J Geophys Res-Solid Earth, 118: 5738–5752
Thomas C W, Liu Q, Agee C B, Asimow P D, Lange R A. 2012. Multitechnique equation of state for Fe2SiO4 melt and the density of Febearing silicate melts from 0 to 161 GPa. J Geophys Res, 117: 10206
Ueki K, Iwamori H. 2016. Density and seismic velocity of hydrous melts under crustal and upper mantle conditions. Geochem Geophys Geosyst, 17: 1799–1814
Urakawa S, Sakamaki T, Ohtani E. 2006. Anomalous compression of basaltic magma: Implication to pressure-induced structural change in silicate melt. Spring-8 Res Front. 113–114
van Kan Parker M, Agee C B, Duncan M S, van Westrenen W. 2011. Compressibility of molten Apollo 17 orange glass and implications for density crossovers in the lunar mantle. Geochim Cosmochim Acta, 75: 1161–1172
van Kan Parker M, Sanloup C, Sator N, Guillot B, Tronche E J, Perrillat J P, Mezouar M, Rai N, van Westrenen W. 2012. Neutral buoyancy of titanium-rich melts in the deep lunar interior. Nat Geosci, 5: 186–189
van Kan Parker M, Sanloup C, Tronche E J, Perrillat J P, Mezouar M, Rai N, van Westrenen W. 2010. Calibration of a diamond capsule cell assembly for in situ determination of liquid properties in the Paris-Edinburgh press. High Pressure Res, 30: 332–341
Vander Kaaden K E, Agee C B, McCubbin F M. 2015. Density and compressibility of the molten lunar picritic glasses: Implications for the roles of Ti and Fe in the structures of silicate melts. Geochim Cosmochim Acta, 149: 1–20
Wakabayashi D, Funamori N. 2013. Equation of state of silicate melts with densified intermediate-range order at the pressure condition of the Earth’s deep upper mantle. Phys Chem Miner, 40: 299–307
Wakabayashi D, Funamori N, Sato T, Sekine T. 2014. Equation of state for silicate melts: A comparison between static and shock compression. Geophys Res Lett, 41: 50–54
Wang Y. 2010. Large volume presses for high-pressure studies using synchrotron radiation. In: Boldyreva E, Dera P, eds. High-Pressure Crystallography. NATO Science for Peace and Security Series B: Physics and Biophysics. Dordrecht: Springer. 81–96
Wang Y, Rivers M, Sutton S, Nishiyama N, Uchida T, Sanehira T. 2009. The large-volume high-pressure facility at GSECARS: A “Swiss-armyknife” approach to synchrotron-based experimental studies. Phys Earth Planet Inter, 174: 270–281
Wang Y, Shen G. 2014. High-pressure experimental studies on geo-liquids using synchrotron radiation at the Advanced Photon Source. J Earth Sci, 25: 939–958
Wang Y B. 2006. Combining the large-volume press with synchrotron radiation: Applications to in-situ studies of Earth materials under high pressure and temperature. Earth Sci Front, 13: 1–36
Williams Q, Garnero E J. 1996. Seismic evidence for partial melt at the base of Earth’s mantle. Science, 273: 1528–1530
Wolf A S, Asimow P D, Stevenson D J. 2015. Coordinated Hard Sphere Mixture (CHaSM): A simplified model for oxide and silicate melts at mantle pressures and temperatures. Geochim Cosmochim Acta, 163: 40–58
Yamazaki D, Ito E, Yoshino T, Tsujino N, Yoneda A, Guo X, Xu F, Higo Y, Funakoshi K. 2014. Over 1Mbar generation in the Kawai-type multianvil apparatus and its application to compression of (Mg0.92Fe0.08)SiO3 perovskite and stishovite. Phys Earth Planet Inter, 228: 262–267
Yasuda A, Fujii T, Kurita K. 1994. Melting phase relations of an anhydrous mid-ocean ridge basalt from 3 to 20 GPa: Implications for the behavior of subducted oceanic crust in the mantle, J Geophys Res, 99: 9401–9414
Yu T, Wang Y, Rivers M L. 2016. Imaging in 3D under pressure: A decade of high-pressure X-ray microtomography development at GSECARS. Prog Earth Planet Sci, 3: 17
Zhang X, Liu Y G, Song W, Wang Z G, Xie H S. 2013. Research progress on ultrasonic velocity measurement of liquid materials under high pressure. Chin J High Pressure Phys, 27: 239–244
Zinin P V, Prakapenka V B, Burgess K, Odake S, Chigarev N, Sharma S K. 2016. Combined laser ultrasonics, laser heating, and Raman scattering in diamond anvil cell system. Rev Sci Instrum, 87: 123908
Acknowledgements
Constructive comments made by Yongfei Zheng, the chief editor, two anonymous reviewers, and Haoran Ma from School of Earth and Space Sciences, Peking University, which greatly improved the quality of this manuscript, are highly appreciated. This work was supported by the National Natural Science Foundation of China (Grant Nos. 40972028, 41520104004, and 41672036).
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Hou, J., Liu, Q. Theoretical models and experimental determination methods for equations of state of silicate melts: A review. Sci. China Earth Sci. 62, 751–770 (2019). https://doi.org/10.1007/s11430-017-9325-3
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DOI: https://doi.org/10.1007/s11430-017-9325-3